A comprehensive characterization of fracture in unit cell open foams generated from Triply Periodic Minimal Surfaces

The main scope of the proposed study is to assess the occurrence of fracture in Triply Periodic Minimal Surfaces (TPMS) foams subjected to compressive loading. TPMS, developed by the mathematics community, may be exploited as a backbone for developing a new class of foams with open porosity for a wide range of engineering and biomedical applications. Therefore, a comprehensive analysis of their fracture response is fundamental and is herein attempted. To this aim, a 3D phase field model is herein proposed and applied to TPMS foam structures under compression, with the goal to predict critical points for crack nucleation, potential crack paths, and the stiffness and maximum force of the unit cell, which can be related to the apparent Young's modulus and apparent strength of a macro-scale composite made of such TPMS unit cells. A careful mesh sensitivity analysis was conducted on the specimens, to provide guidelines on how to identify the optimal finite element discretization consistent with the internal length scale parameter of the phase field approach to fracture. The major predicted mechanical properties for five different TPMS open foams, and for different levels of porosity, are summarized in Ashby plots. The predicted trends are in agreement with previous results on TPMS taken from the literature and show that TPMS can outperform standard Aluminium open foams.